WASHINGTON — Even as liberals urge President Barack Obama to demand bold, far-reaching changes to the nation’s health care system, the White House signaled openness Thursday to compromises that might attract moderate congressional Democrats as well as some Republicans.

Obama believes in “fundamental principles” about overhauling health care, top presidential adviser David Axelrod said, but “he’s not dogmatic about how we get there.”

Axelrod’s comments did not definitively answer how hard Obama will push for the most ambitious parts of his proposal, including health insurance for virtually all Americans and a government-run plan to compete with private insurers. But his diplomatic tone was in keeping with the administration’s approach of refusing to flatly demand several parts that are dear to Democratic activists who helped elect him.

Those are the type of conciliatory hints that frustrate many liberals. They fear Obama will dilute the bold health care proposals he campaigned for, even though Democrats control the House, Senate and White House.

The plan has been floated by Republican Sen. Olympia Snowe of Maine, who is often seen as the most likely GOP lawmaker to support a primarily Democratic-crafted health bill. She would have nonprofit agencies offer health insurance only if private insurers could not cover 95 percent of the people in their regions with plans costing no more than about 15 percent of the person’s or household’s annual income.

Many Democrats want prompt creation of a government-run program to compete with private insurers, who stand to gain millions more customers if Congress mandates coverage of the nation’s uninsured.

Obama has often said he favors such a “public option.” But he and his aides have repeatedly stopped short of saying he would sign no bill without it.

Liberals hope the administration’s conciliatory words will eventually give way to a forceful move to enact a far-reaching bill, even if it draws no GOP votes.

Former President Bill Clinton told Esquire Magazine that Obama should forge ahead with his health care proposals. “I wouldn’t even worry about the Republicans,” he said. Obama is doing the right thing, Clinton said, “even though he’s jamming a lot of change down the system.”

Some are warning Obama not to take them for granted.

The Congressional Progressive Caucus, composed of 83 liberal lawmakers, sent Obama a letter Thursday saying a health bill “without a robust public option will not achieve the health reform this country so desperately needs. We cannot vote for anything less.”

But some moderate Democrats in the House and Senate are wary of a government-run insurance plan. It might amass enough leverage over doctors, drug companies and others to eventually drive private insurers out of business, they say.

The Congressional Black Caucus called Thursday on Obama to show “unwavering support” for “a strong public health option” and the full funding of health care expansions, included in a pending House bill.

Vice President Joe Biden said Thursday that it will be difficult to find a consensus on remaking the health care system. But he also predicted that “we’re going to get there.”

Meanwhile, a top Republican player in the health care debate said Americans should expect a rather modest bill from Congress this fall. Sen. Charles Grassley of Iowa, one of three GOP negotiators seeking a bipartisan bill in the Senate Finance Committee, told Iowa radio station KMCH: “It may be kind of miniature to what we’re talking about.”